How does Linux handle multiple consecutive path separators (/home////username///file)?

Multiple slashes are allowed and are equivalent to a single slash. From the Single Unix specification (version 4), base definitions §3.271 pathname: “Multiple successive slashes are considered to be the same as one slash.”

There is one exception: If a pathname begins with two successive slash characters, the first component following the leading slash characters may be interpreted in an implementation-defined manner. (ref: base definitions §4.13 pathname resolution). Linux itself doesn't do this, though some applications might, and other unix-ish system do (e.g. Cygwin).

A trailing / at the end of a pathname forces the pathname to refer to a directory. In (POSIX 1003.1-2001 (Single Unix v4) base definitions §4.11 pathname resolution, a trailing / is equivalent to a trailing /.. POSIX 1003.1-2008 (Single Unix v4) base definitions §4.13 removes the requirement to make it equivalent to /., in order to cope with non-existing directories (e.g. mkdir foo/ is required to work, whereas mkdir foo/. wouldn't — see the rationale for the change).

For programs that act on a directory entry, if foo is a symbolic link to a directory, then passing foo/ is a way to make the program act on the directory instead of the symbolic link.

¹ _{Note that this applies for pathname resolution only, i.e. when accessing files. Filename manipulations may work differently. For example basename and dirname ignore trailing slashes.}

The OS doesn't appear to care about it either, having just tried out a C program with a direct syscall to open with a // in the path.

You can use the python library function os.path.normpath to normalize it though, which saves you having to scan through the string looking for extras. Other languages have similar functions.

http://docs.python.org/library/os.path.html#os.path.normpath

On all Unix systems that I've seen it's the same as a single /, but the Unix standard specifies that

A pathname that begins with two successive slashes may be interpreted in an implementation-defined manner, although more than two leading slashes shall be treated as a single slash.

so it may be handled specially, depending on your system. (Some older Unix versions used a double leading / for remote filesystem access, and there may still be some that do.)